有色噪声作用下的卡尔曼滤波

Kalman Filtering of Linear System with Colored Noises

摘要: 利用GPS载波相位三差观测量进行动态定位(或精密导航),就必须研究有色噪声滤波的理论问题。根据需求,推导了动态噪声、观测噪声为有色噪声的线性系统滤波公式,并证明白噪声卡尔曼滤波是有色噪声卡尔曼滤波的特例,或者说有色噪声的卡尔曼滤波是白噪声卡尔曼滤波的推广。

Abstract: To solve the problem of colored noise filtering to do the precise dynamic positioning(or navagation) by use of the three phase difference of GPS carrier waves.The linear filters with dynamic colored noises and observational colored noises are derived and it may be proved that the Kalman filtering with dynamic white noises is the special case of Kalman filtering with dynamic colored noises,the Kalman filtering with observational white noises is the special case of Kalman filtering with observational colored noises.